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Q. 22

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Found in: Page 156

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Graph the function $f$ by starting with the graph of $y={x}^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.$f\left(x\right)=\left(x-3{\right)}^{2}-10$

The required graph is shown below:

See the step by step solution

## Step 1. Given information.

The given function is:

$f\left(x\right)=\left(x-3{\right)}^{2}-10$

## Step 2. Determine the transformations used.

In the function $f\left(x\right)=a\left(x-h{\right)}^{2}+k,a$ is a constant and $\left(h,k\right)$ is the vertex.

In the given function $a=1,h=3,k=-10$. It means the graph of the given function is a parabola that opens up and has its vertex at $\left(3,-10\right)$ and its axis of symmetry is the line $x=3$.

The graph of $y={x}^{2}$ shifts 3 units right and 10 units down.

First plot the graph of $y={x}^{2}$ then shift it 3 units right and then shift the resulted graph 10 units down to get the graph of the function $f\left(x\right)=\left(x-3{\right)}^{2}-10$.

## Step 3. Draw the graph.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.